{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "436f9cba",
   "metadata": {},
   "source": [
    "# Transpose arrays and swap axes\n",
    "\n",
    "Transpose is a special form of reshaping that also provides a view of the underlying data without copying anything. Arrays have the [Transpose](https://numpy.org/doc/stable/reference/generated/numpy.transpose.html) method and also the special [T](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.T.html) attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8f1170da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "864383e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.arange(16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1252c797",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0184cebd",
   "metadata": {},
   "outputs": [],
   "source": [
    "reshaped_data = data.reshape((4, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3045e448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reshaped_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fce7877b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  4,  8, 12],\n",
       "       [ 1,  5,  9, 13],\n",
       "       [ 2,  6, 10, 14],\n",
       "       [ 3,  7, 11, 15]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reshaped_data.T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a056b80b",
   "metadata": {},
   "source": [
    "[numpy.dot](https://numpy.org/doc/stable/reference/generated/numpy.dot.html) returns the scalar product of two arrays, for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a315f3cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[224, 248, 272, 296],\n",
       "       [248, 276, 304, 332],\n",
       "       [272, 304, 336, 368],\n",
       "       [296, 332, 368, 404]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(reshaped_data.T, reshaped_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9748f100",
   "metadata": {},
   "source": [
    "The `@` infix operator is another way to perform matrix multiplication. It implements the semantics of the `@` operator introduced in Python 3.5 with [PEP 465](https://peps.python.org/pep-0465/) and is an abbreviation of [np.matmul](https://numpy.org/doc/stable/reference/generated/numpy.matmul.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "452cc86c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(1240)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.T @ data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ed92d44",
   "metadata": {},
   "source": [
    "For higher dimensional arrays, [transpose](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.transpose.html) accepts a tuple of axis numbers to swap the axes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "eabf771b",
   "metadata": {},
   "outputs": [],
   "source": [
    "array_3d = np.arange(16).reshape((2, 2, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "81d17b52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "edff77ed",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[ 4,  5,  6,  7],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_3d.transpose((1, 0, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87fa49b0",
   "metadata": {},
   "source": [
    "Here the axes have been reordered with the second axis in first place, the first axis in second place and the last axis unchanged."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0b351e",
   "metadata": {},
   "source": [
    "`ndarray` also has a [swapaxes](https://numpy.org/doc/stable/reference/generated/numpy.swapaxes.html) method that takes a pair of axis numbers and swaps the specified axes to rearrange the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4d1abfc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  4],\n",
       "        [ 1,  5],\n",
       "        [ 2,  6],\n",
       "        [ 3,  7]],\n",
       "\n",
       "       [[ 8, 12],\n",
       "        [ 9, 13],\n",
       "        [10, 14],\n",
       "        [11, 15]]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_3d.swapaxes(1, 2)"
   ]
  }
 ],
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